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## Main Question or Discussion Point

**[SOLVED] Representation of j=1 rotation matrix**

The derivation of this involves the use of the following fact for j=1:

[atex]\frac{J_y}{\hbar} = (J_y/\hbar)^3[/itex].

Is there a simple way to see this other than slogging through the algebra by expanding out the RHS using [itex]J_y = \frac{1}{2i}(J_+ - J_i)[/itex] and [itex]J_{\pm}|jm\rangle = \hbar\sqrt{(j\mp m)(j \pm m + 1)}| j,m\pm 1\rangle[/itex]?